Shadow from camera vs shadow from reflection
So for this I would use render layers. This means you can't really view the effect 'live' in the viewport, but it will be applied when rendered and composited.

I have 2 render layers:


Render layer 1, called 'Main', renders layer 1 which holds the sphere and light only.





Render layer 2, called 'Floor', renders layer 2 which is the floor object and excludes layer 3, which is the red plane.




'Transparent' must be enabled in film section of the Render tab to allow layers to be composited together.



Note: All 3 scene layers should be made visible before rendering. All 3 layers are required, the render layers take care of what appears in the render.

'Main' render layer will only include the sphere, but will still be effected by the other layers, so will include the plane and floor in the reflection.

'Floor' render layer will only include the floor object and will only be effected by layer 1 because red object is excluded on layer 3.

These render layers can then be combined in the compositor:



Which results in: